Question 200
A communications network consisting of some terminals is called a 3-connector if among any three terminals, some two of them can directly communicate with each other. A communications network contains a windmill with $n$ blades if there exist $n$ pairs of terminals $\{x_1, y_1\}, \dots, \{x_n, y_n\}$ such that each $x_i$ can directly communicate with the corresponding $y_i$ and there is a hub terminal that can directly communicate with each of the $2n$ terminals $x_1, y_1, \dots, x_n, y_n$. Determine the minimum value of $f(n)$, in terms of $n$, such that a 3-connector with $f(n)$ terminals always contains a windmill with $n$ blades.